Generation of VLF Mode Instability by Generalized Distribution Function in the Presence of Parallel AC Electric Field in Uranus

VLF （very low frequency） mode instability with parallel AC electric field was studied for generalized loss-cone distribution with an index j, which is reducible to bi-Maxwellian, loss- cone and delta function for j = 0, 1 and co. The particle trajectories and dispersion relation are obtained through a kinetic approach and method of characteristic solutions. The calculations are compared with the observations of low frequency waves of Voyager 2. The growth rate of plasma parameters suited to magnetosphere of Uranus is obtained. It is inferred that the magnitude as well as frequency of AC （alternating current） field increases the growth rate and widen the band width significantly. In addition to temperature anisotropy, particles in plasma having generalized loss-cone distribution provide an additional source of energy.

Effect of wall-cooling on Mack-mode instability in high speed flat-plate boundary layers

The instability of the Mack mode is destabilized by wall-cooling in a high speed boundary layer. The aim of this paper is to study the mechanism of the wall cooling effect on the Mack mode instability by numerical methods. It is shown that the wall-cooling can destabilize the Mack mode instability, similar to the previous conclusions with the exception that the Mack mode instability can be stabilized by wall-cooling if the wall temperature is extremely low. The reversed wall temperature is related to a freestream condition. If the Mach number increases to a large enough value, e.g., about 7, the reversed wall temperature will tend to be zero. It seems that the Mack mode instability is determined by the region between the boundary layer edge and the critical layer. When the wall temperature decreases, this region becomes wider, and the boundary layer becomes more unstable. Additionally, a relative supersonic unstable mode can be observed when the velocity of the critical layer is less than 1 - liMa or is cancelled by the wall-cooling effect. These results provide a deeper understanding on the wall-cooling effect in high speed boundary layers.

Application of Galerkin spectral method for tearing mode instability

Magnetic reconnection and tearing mode instability play a critical role in many physical processes.The application of Galerkin spectral method for tearing mode instability in two-dimensional geometry is investigated in this paper.A resistive magnetohydrodynamic code is developed,by the Galerkin spectral method both in the periodic and aperiodic directions.Spectral schemes are provided for global modes and local modes.Mode structures,resistivity scaling,convergence and stability of tearing modes are discussed.The effectiveness of the code is demonstrated,and the computational results are compared with the results using Galerkin spectral method only in the periodic direction.The numerical results show that the code using Galerkin spectral method individually allows larger time step in global and local modes simulations,and has better convergence in global modes simulations.

On the mechanism by which nose bluntness suppresses second-mode instability

A physical mechanism by which nose bluntness suppresses second-mode instability is proposed.Considered are 7 degree half-angle straight cones with nose bluntness radii of 0.15 mm, 3.556 mm,5 mm, 9.525 mm, 12.7 mm and 25.4 mm at tunnel conditions relevant to the AFOSR-Notre Dame Large Mach 6 Quiet Tunnel. It is shown that second-mode suppression is achieved via entropy layer modulation of the basic state density gradient. A weakening of the density gradient disrupts the acoustic resonance necessary to sustain second-mode growth. These results are consistent with the thermoacoustic interpretation which posits that second-mode instability can be modeled as thermoacoustic resonance of acoustic energy trapped within an acoustic impedance well.Furthermore, the generalized inflection point criterion of Lees and Lin is applied to develop a criterion for the existence of second-mode instability based on the strength of the basic state density gradient.

Transverse mode instability mitigation in a high-power confined-doped fiber amplifier with good beam quality through seed laser control

In this work,a confined-doped fiber with the core/inner-cladding diameter of 40/250μm and a relative doping ratio of 0.75 is fabricated through a modified chemical vapor deposition method combined with the chelate gas deposition technique,and subsequently applied in a tandem-pumped fiber amplifier for high-power operation and transverse mode instability(TMI)mitigation.Notably,the impacts of the seed laser power and mode purity are preliminarily investigated through comparative experiments.It is found that the TMI threshold could be significantly affected by the seed laser mode purity.The possible mechanism behind this phenomenon is proposed and revealed through comprehensive comparative experiments and theoretical analysis.Finally,a maximum output power of 7.49 kW is obtained with the beam quality factor of approximately 1.83,which is the highest output power ever reported in a forward tandem-pumped confined-doped fiber amplifier.This work could provide a good reference and practical solution to improve the TMI threshold and realize high-power high-brightness fiber lasers.

INSTABILITY OF HAGEN-POISEUILLE FLOW FOR NON-AXISYMMETRIC MODE

An investigation is described for instability problem of flow through a pipe of circular cross section. As a disturbance motion, we consider a general non-axisym-metric mode. An associated amplitude or modulation equation has been derived for this disturbance motion. This equation belongs to a diffusion type.The coefficient of it can be negative while Reynolds number increases, because of the complex interaction between molecular diffusion and convection. The negative diffusivity, when it occurs, causes a concentration and focussing of energy within decaying slugs, acting as a role of reversing natural decays.

Sliding behaviors of the trapezoidal roof rock block under a lateral dynamic disturbance

The surrounding rock of underground space is always affected by external dynamic disturbance from the side position,such as blasting vibration from a stope at the same level or seismic waves from adjacent strata.A series of laboratory tests,numerical simulations and theoretical analyses were carried out in this study to disclose the sliding mechanism of roof rock blocks under lateral disturbance.Firstly,the experiments on trapezoidal key block under various clamping loads and disturbance were conducted,followed by numerical simulations using the fast Lagrangian analysis of continua(FLAC3D).Then,based on the conventional wave propagation model and the classical shear-slip constitutive model,a theoretical model was proposed to capture the relative displacement between blocks and the sliding displacement of the key block.The results indicate that the sliding displacement of the key block increased linearly with the disturbance energy and decreased exponentially with the clamping load when the key block was disturbed to slide(without instability).Meanwhile,when the key block was disturbed to fall,two types of instability process may appear as immediate type or delayed type.In addition,the propagation of stress waves in the block system exhibited obvious low-velocity and lowfrequency characteristics,resulting in the friction reduction effect appearing at the contact interface,which is the essential reason for the sliding of rock blocks.The results can be applied to practical underground engineering and provide valuable guidance for the early detection and prevention of rockfalling disasters.

Linear Analysis of Longshore Currents Instability over Mild Slopes

Longshore current instability is important to nearshore hydrodynamic and sediment transport. This paper investigates the longshore current instability growth model based experimental data with different velocity profiles of slopes1:100 and 1:40 by adopting a linear shear instability model with the bottom friction effects. The results show that:(1)Only backshear mode exists in the instability of longshore current for slope 1:40 and frontshear and backshear modes may exist slope 1:100.(2) The peaks of linear instability growth mode for slope 1:100 correspond to three cases: the dominant peak is formed by the joint action of both frontshear and backshear, or by backshear alone without the existence of the smaller peak or formed by either the frontshear or backshear.(3) Bottom friction can decrease the corresponding unstable growth rate but it cannot change the unstable fluctuation period. The results of fluctuation period, wavelength and spatial variation obtained by the analysis of linear shear instability are in good agreement with experimental results.

Experimental investigation on flow modes of electrospinning

Electrospinning experiments are performed by using a set of experimental apparatus, a stroboscopic system is adopted for capturing instantaneous images of the cone- jet configuration. The cone and the jet of aqueous solutions of polyethylene oxide （PEO） are formed from an orifice of a capillary tube under the electric field. The viscoelastic con- stitutive relationship of the PEO solution is measured and discussed. The phenomena owing to the jet instability are described, five flow modes and corresponding structures are obtained with variations of the fluid flow rate Q, the electric potential U and the distance h from the orifice of the cap- illary tube to the collector. The flow modes of the cone-jet configuration involves the steady bending mode, the rotat- ing bending mode, the swinging rotating mode, the blurring bending mode and the branching mode. Regimes in the Q-U plane of the flow modes are also obtained. These results may provide the fundamentals to predict the operating conditions expected in practical applications.

The effect of G?rtler instability on hypersonic boundary layer transition

The evolution of Gortler vortices and its interaction with other instabilities are investigated in this paper. Both the Mack mode and the Gortler mode exist in hypersonic boundary-layer flows over concave surfaces, and their interactions are crucially important in boundary layer transition. We carry out a direct numerical simulation to explore the interaction between the GOrtler and the oblique Mack mode. The results indicate that the interaction between the forced Gortler mode and the oblique Mack mode promotes the onset of the transition. The forced oblique Mack mode is susceptible to nonlinear interaction. Because of the development of the GOrtler mode, the forced Mack mode and other harmonic modes are excited.

5 kW-level single-mode fiber amplifier based on low-numerical-aperture fiber

A low-numerical-aperture(NA)concept enables large-mode-area fiber with better single-mode operation ability,which is beneficial for transverse mode instability and nonlinear effects suppression.In this contribution,we reported a high-power fiber amplifier based on a piece of self-developed large-mode-area low-NA fiber with a core NA of 0.049 and a core/inner cladding diameter of 25/400μm.The influence of the pump wavelength and fiber length on the power scaling potential of the fiber amplifier is systematically investigated.As a result,an output of 4.80 kW and a beam quality factor of~1.33 were finally obtained,which is the highest output power ever reported in a fiber amplifier exploiting the low-NA fiber.The results reveal that low-NA fibers have superiority in power scaling and beam quality maintenance at high power levels.

THREE-DIMENSIONAL AXISYMMETRIC FLOW IN PERFECTLY PLASTIC METALS

A method is presented for solving the three-dimensional axisymmet- ric field equations for a perfectly plastic material which obeys the von-Mises yield criterion and the Levy-Mises flow law. The method is used for the particular case in which a small axisymmetric perturbed flow is superposed on a uniform flow without flow reversal taking place. The method then leads to solving a fourth order differen- tial equation for the velocity potential. The special case of a thick cylindrical shell under compressive flow is examined. The solution so obtained, being derived from the three dimensional theory, includes a correct treatment of transverse shear distor- tion. A preferred mode of instability is identified having a wave-length in reasonable agreement with that obtained experimentally by other workers.

Static and dynamic mode evolution in high-power distributed side-coupled cladding-pumped fiber amplifiers

We present a theoretical study of mode evolution in high-power distributed side-coupled cladding-pumped(DSCCP)fiber amplifiers.A semi-analytical model taking the side-pumping schemes,transverse mode competition,and stimulated thermal Rayleigh scattering into consideration has been built,which can model the static and dynamic mode evolution in high-power DSCCP fiber amplifiers.The mode evolution behavior has been investigated with variation of the fiber amplifier parameters,such as the pump power distribution,the length of the DSCCP fiber,the averaged coupling coefficient,the number of the pump cores and the arrangement of the pump cores.Interestingly,it revealed that static mode evolution induced by transverse mode competition is different from the dynamic evolution induced by stimulated thermal Rayleigh scattering.This shows that the high-order mode experiences a slightly higher gain in DSCCP fiber amplifiers,but the mode instability thresholds for DSCCP fiber amplifiers are higher than those for their end-coupled counterparts.By increasing the pump core number and reducing the averaged coupling coefficient,the mode instability threshold can be increased,which indicates that DSCCP fibers can provide additional mitigation strategies of dynamic mode instability.

1.3 kW monolithic linearly polarized single-mode master oscillator power amplifier and strategies for mitigating mode instabilities

We report on the high-power amplification of a 1064 nm linearly polarized laser in an all-fiber polarizationmaintained master oscillator power amplifier,which can operate at an output power level of 1.3 kW.The beam quality(M^2) was measured to be <1.2 at full power operation.The polarization extinction rate of the fiber amplifier was measured to be above 94% before mode instabilities(MIs) set in,which reduced to about 90% after the onset of MI.The power scaling capability of strategies for suppressing MI is analyzed based on a semianalytical model,the theoretical results of which agree with the experimental results.It shows that mitigating MI by coiling the gain fiber is an effective and practical method in standard double-cladding large mode area fiber,and,by tight coiling of the gain fiber to the radius of 5.5 cm,the MI threshold can be increased to three times higher than that without coiling or loose coiling.Experimental studies have been carried out to verify the idea,which has proved that MI was suppressed successfully in the amplifier by proper coiling.

High-power single-frequency fiber amplifiers:progress and challenge[Invited]

Unlike conventional continuous-wave lasers with wide spectra,the amplification of single-frequency lasers in optical fibers is much more difficult owing to the ultra-high power spectral density induced nonlinear stimulated Brillouin scattering effect.Nevertheless,over the past two decades much effort has been devoted to improving the power scaling and performance of high-power single-frequency fiber amplifiers.These amplifiers are mostly driven by applications,such as high precision detection and metrology,and have benefited from the long coherence length,low noise,and excellent beam quality of this type of laser source.In this paper,we review the overall development of high-power single-frequency fiber amplifiers by focusing on its progress and challenges,specifically,the strategies for circumventing the stimulated Brillouin scattering and transverse mode instability effects that,at present,are the major limiting factors of the power scaling of the single-frequency fiber amplifiers.These factors are also thoroughly discussed in terms of free-space and all-fiber coupled architecture.In addition,we also examine the noise properties of single-frequency fiber amplifiers,along with corresponding noise reducing schemes.Finally,we briefly envision the future development of high-power single-frequency fiber amplifiers.

1.2 kW all-fiber narrow-linewidth picosecond MOPA system

Achieving an all-fiber ultra-fast system with above kW average power and mJ pulse energy is extremely challenging.This paper demonstrated a picosecond monolithic master oscillator power amplifier system at a 25 MHz repetition frequency with an average power of approximately 1.2 kW,a pulse energy of approximately 48μJ and a peak power of approximately 0.45 MW.The nonlinear effects were suppressed by adopting a dispersion stretched seed pulse(with a narrow linewidth of 0.052 nm)and a multi-mode master amplifier with an extra-large mode area;then an ultimate narrow bandwidth of 1.32 nm and a moderately broadened pulse of approximately 107 ps were achieved.Meanwhile,the great spatio-temporal stability was verified experimentally,and no sign of transverse mode instability appeared even at the maximum output power.The system has shown great power and energy capability with a sacrificed beam propagation product of 5.28 mm·mrad.In addition,further scaling of the peak power and pulse energy can be achieved by employing a lower repetition and a conventional compressor.

Novel constant-cladding tapered-core ytterbium-doped fiber for high-power fiber laser oscillator

Power scaling based on traditional ytterbium-doped fibers(YDFs)is limited by optical nonlinear effects and transverse mode instability(TMI)in high-power fiber lasers.Here,we propose a novel long tapered fiber with a constant cladding and tapered core(CCTC)along its axis direction.The tapered-core region of the fiber is designed to enhance the stimulated Raman scattering(SRS)threshold and suppress higher-order mode resonance in the laser cavity.The CCTC YDF was fabricated successfully with a modified chemical vapor deposition(MCVD)method combined with solution doping technology,which has a cladding diameter of 400µm and a varying core with a diameter of~24μm at both ends and~31μm in the middle.To test the performance of the CCTC fiber during high-power operation,an all-fiber laser oscillator based on a CCTC YDF was investigated experimentally.As a result,a maximum output power of 3.42 kW was achieved with an optical-to-optical efficiency of 55.2%,although the TMI effect was observed at an output power of~3.12 kW.The measured beam quality(M^(2)factor)was~1.7,and no sign of the Raman component was observed in the spectrum.We believe that CCTC YDF has great potential to simultaneously mitigate the SRS and TMI effects,and further power scaling is promising by optimizing the structure of the YDF.

JUMPING INSTABILITIES IN THE POST-BUCKLING OF A BEAM ON A PARTIAL NONLINEAR FOUNDATION

Mode jumping is an instability phenomenon in the post-buckling region, which causes a sudden change in the equilibrium configuration and is thus harmful to structure. The con- figuration of a partial elastic foundation can directly induce mode coupling from the buckling stage and through the whole post-buckling region. The mode coupling effect due to the configuration of partial foundation on mode jumping is investigated and demonstrated to be an important factor of determining mode jumping. By properly choosing the partial elastic foundation configuration, mode jumping can be avoided.